The ordinal Nash equilibrium (ONE) provides one possibility to analyze strategies in ordinal games such as matching markets [1]}, [2]}, [3]}. ONE only takes purely ordinal preferences into account. One must consider every possible vNM function that abides by the underlying preference structure. Not surprisingly, ordinal Nash equilibria rarely exist.
In most applications, the case of agents having no intensity about their preferences between different choices is unlikely. But then agents' strategies cannot be studied without taking these intensities into account.
[4]} introduced the concept of Bayesian games that express incomplete information via different types with a corresponding prior distribution over the types. We use this concept to model uncertainty about players' preferences. However, we differ from Harsanyi in assuming that uncertainty over players' types persists until the ex-post stage.
